Quotient de deux nombres complexes

9-i

Nouvel énoncé

partie réelle:

partie imaginaire

  \text{ i}

3+2*i

Bonne réponse

\text{Calculez les valeurs exactes des deux réels  } x \text{ et } y  \text{ afin que le quotient suivant ait pour forme algébrique }x+y\text{ i}.

\text{ et } y =

x=

Valider ce résultat

Voir l'aide n°1

Voir l'aide n°3

Voir l'aide n°2

Mauvaise réponse

RAZ

Dans cette série d'exercices vous allez devoir déterminer la forme
algébrique de quotients de deux nombres complexes.

Mathématiques à Valin

3+3i

9-i

NA1

NA2

Juste

Faux

2+i

2-3i

NB1

NB2=

Juste

Faux

2+i

3-i

NC1

NC2

Faux

Juste

Lignes de calcul:

(3+4i)

-7i

3+3i

2+i

2-3i

2+i

3-i

  \frac{ 7 }{ 3 } 

 5

 +

Commencer l'exercice

\ovalbox{\text{Dernier exercice}}

d = -4 (slider from -7 to 7, step 1)
c = -2 (slider from -7 to 5, step 1)
a = -5 (slider from -7 to 7, step 1)
b = 5 (slider from -7 to 5, step 1)
repim: ((b * c) - (a * d)) / (c^(2) + d^(2))
absrepim: abs(repim)
trep1im = SurdText(absrepim)
den = (1, 0)
num = (0, 0)
ta = If(a ≟ 0, "", "" + a)
tc = If(c ≟ 0, "", "" + c)
tdi = If(d ≟ 0, "", If[d ≟ 1, "+\text{ i}", If[d ≟ -1, "-\text{ i}", If[d > 1, "+" + d + "\text{ i}", "" + d + "\text{ i}"]]])
tbi = If(b ≟ 0, "", If[b ≟ 1, "+\text{ i}", If[b ≟ -1, "-\text{ i}", If[b > 1, "+" + b + "\text{ i}", "" + b + "\text{ i}"]]])
tbi2 = If(b ≟ 0, "", If[b ≟ 1, "\text{ i}", If[b ≟ -1, "-\text{ i}", If[b > 1, "" + b + "\text{ i}", "" + b + "\text{ i}"]]])
tnum = If(a ≠ 0, ta + tbi, tbi2)
tdi2 = If(d ≟ 0, "", If[d ≟ 1, "\text{ i}", If[d ≟ -1, "-\text{ i}", If[d > 1, "" + d + "\text{ i}", "" + d + "\text{ i}"]]])
tden = If(c ≠ 0, tc + tdi, tdi2)
re = 5
im = 2.3333333333333335
absre: abs(re)
mathre1 = SurdText(absre)
ChampTexte1 = Textfield(ttre)
ChampTexte2 = Textfield(ttim)
absim: abs(im)
mathim1 = SurdText(absim)
zero = If(re ≟ 0 ∧ im ≟ 0 ∨ re ≟ 0 ∧ (¬Defined[im]) ∨ (¬Defined[re]) ∧ im ≟ 0, "0", "")
re2 = If(Defined[re], re, 0)
im2 = If(Defined[im], im, 0)
repre: ((a * c) + (b * d)) / (c^(2) + d^(2))
quotientjuste: repre ≟ re2 ∧ repim ≟ im2
oppd: (-d)
tconjdi = If(oppd ≟ 0, "", If[oppd ≟ 1, "+\text{ i}", If[oppd ≟ -1, "-\text{ i}", If[oppd > 1, "+" + oppd + "\text{ i}", "" + oppd + "\text{ i}"]]])
topdi2 = If(oppd ≟ 0, "", If[oppd ≟ 1, "\text{ i}", If[oppd ≟ -1, "-\text{ i}", If[oppd > 1, "" + oppd + "\text{ i}", "" + oppd + "\text{ i}"]]])
tconjden = If(c ≠ 0, tc + tconjdi, topdi2)
par1num = If((a * b) ≠ 0, "(", "")
par2num = If((a * b) ≠ 0, ")", "")
par1den = If((c * d) ≠ 0, "(", If[c > 0, "\times", If[c  <  0, "\times(", If[d  <  0, "\times", "\times("]]])
par2den = If((c * d) ≠ 0, ")", If[c > 0, "\", If[c  <  0, ")", If[d  <  0, "", ")"]]])
par3d = If((c * d) ≠ 0, "(", "")
par4d = If((c * d) ≠ 0, ")")
relnum: (a * c) + (b * d)
imnum: (b * c) - (a * d)
modul: c^(2) + d^(2)
timnum = If(imnum  <  -1, "" + imnum + "\text{ i}", If[imnum ≟ -1, "-\text{ i}", If[imnum ≟ 1, "+\text{ i}", If[imnum > 1, "+" + imnum + "\text{ i}"]]])
absrepre: abs(repre)
trep1re = SurdText(absrepre)
trepre = If(repre  <  0, "-" + trep1re, trep1re)
trepim = If(repim ≟ 1, "\text{ i}", If[repim ≟ -1, "-\text{ i}", If[repim  <  0, "-" + trep1im + "\text{ i}", If[repim > 0, "" + trep1im + "\text{ i}"]]])
absrep1im: abs(repim)
pludansrep = If((repre ≠ 0) ∧ (repim > 0), "+", "")
testdemande = false
aide1 = false
aide2 = false
aide3 = false
voiraide1 = false
voiraide2 = false
voiraide3 = false
tegal = If(ttre ≟ "" ∧ ttim ≟ "", "", "=")
score = 0
nbexo = 1
gain = 1
pluriel1 = If(score > 1, "s", "")
pluriel2 = If(nbexo > 1, "s", "")
texte10: "" + (LaTeX[score]) + "\text{ exercice}" + (LaTeX[pluriel1]) + " \text{ réussi}" + (LaTeX[pluriel1]) + " \text{ sur } " + (LaTeX[nbexo]) + "\text{ proposé}" + (LaTeX[pluriel2]) + "."
debut = false
texte3_1: "\text{On multiplie numérateur et dénominateur par le conjugué}\\\text{du dénominateur } \text{  :  }\frac{" + (LaTeX[tnum]) + "}{" + (LaTeX[tden]) + "}=\frac{" + (LaTeX[par1num]) + "" + (LaTeX[tnum]) + "" + (LaTeX[par2num]) + "\textcolor{red}{" + (LaTeX[par1den]) + "" + (LaTeX[tconjden]) + "" + (LaTeX[par2den]) + "}}{" + (LaTeX[par3d]) + "" + (LaTeX[tden]) + "" + (LaTeX[par4d]) + "\textcolor{red}{" + (LaTeX[par1den]) + "" + (LaTeX[tconjden]) + "" + (LaTeX[par2den]) + "}} "
texte3: "\text{On utilise l'identité   }  \textcolor{blue}{(a+b\text{ i})(a-b\text{ i})=a^2+b^2}\text{  :  }\\\frac{" + (LaTeX[tnum]) + " }{ " + (LaTeX[tden]) + "}=\frac{" + (LaTeX[par1num]) + "" + (LaTeX[tnum]) + " " + (LaTeX[par2num]) + "" + (LaTeX[par1den]) + "" + (LaTeX[tconjden]) + "" + (LaTeX[par2den]) + "     }{   \textcolor{red}{ (" + (LaTeX[c]) + ")^2+(" + (LaTeX[d]) + ")^2  }}"
texte4: "\text{On obtient : }\frac{" + (LaTeX[tnum]) + "}{" + (LaTeX[tden]) + "}=\frac{" + (LaTeX[relnum]) + "" + (LaTeX[timnum]) + "}{" + (LaTeX[modul]) + "}=" + (LaTeX[trepre]) + "" + (LaTeX[pludansrep]) + "" + (LaTeX[trepim]) + ""
NA1: 3 + (3 * ί) + (0 * ί)
NA2: 9 - ί + (0 * ί)
ChampTexte3 = Textfield(tNA1)
ChampTexte4 = Textfield(tNA2)
ligne1: NA1 / NA2
pointrep: repre + (ί * repim)
ligne1juste: pointrep ≟ ligne1
ChampTexte5 = Textfield(tNB1)
ChampTexte6 = Textfield(tNB2)
NB1: 2 + ί + (0 * ί)
NB2: 2 - (3 * ί) + (0 * ί)
ligne2: NB1 / NB2
ligne2juste: pointrep ≟ ligne2
comandA2: "NA2=" + tNA2new + "+0*i"
NC1: 2 + ί + (0 * ί)
NC2: 3 - ί + (0 * ί)
ChampTexte7 = Textfield(tNC1)
ChampTexte8 = Textfield(tNC2)
ligne3: NC1 / NC2
ligne3juste: pointrep ≟ ligne3
texte5: "=\frac{\phantom{1}" + (LaTeX[tNA1]) + "}{" + (LaTeX[tNA2]) + "}"
texte15: "=\frac{\phantom{1}" + (LaTeX[tNB1]) + "}{" + (LaTeX[tNB2]) + "}"
texte18: "=\frac{\phantom{1}" + (LaTeX[tNC1]) + "}{" + (LaTeX[tNC2]) + "} "
ZERO = (0, 0)
UN = (1, 0)
testligne = false
code = 196
code1: code + 11
code3 = Mod((code * (nbexo + 5)), 991)
code2 = Mod((code * (score + 7)), 991)
codefinal: (1000000 * code1) + (1000 * code2) + code3
texte22: "Code Valin : " + codefinal + ""
code0 = Random(101, 975)
place = NaN
comandA1: "NA1=" + tNA1new + "+0*i"
comandB1: "NB1=" + tNB1new + "+0*i"
comandB2: "NB2=" + tNB2new + "+0*i"
comandC1: "NC1=" + tNC1new + "+0*i"
comandC2: "NC2=" + tNC2new + "+0*i"
texte1: "\frac{" + (LaTeX[tnum]) + "}{" + (LaTeX[tden]) + "}" + (LaTeX[tegal]) + "" + (LaTeX[zero]) + "" + (LaTeX[textemathre]) + "" + (LaTeX[textesignim]) + "" + (LaTeX[textemathim]) + "" + (LaTeX[tii]) + ""
grade: score
notemax: 500